Quantum Continuous Variables
A Primer of Theoretical Methods

Quantum Continuous Variables introduces the theory of continuous variable quantum systems, from its foundations based on the framework of Gaussian states to modern developments, including its applications to quantum information and forthcoming quantum technologies. This new book addresses the theory of Gaussian states, operations, and dynamics in great depth and breadth, through a novel approach that embraces both the Hilbert space and phase descriptions.

The volume includes coverage of entanglement theory and quantum information protocols, and their connection with relevant experimental set-ups. General techniques for non-Gaussian manipulations also emerge as the treatment unfolds, and are demonstrated with specific case studies.

This book will be of interest to graduate students looking to familiarise themselves with the field, in addition to experienced researchers eager to enhance their understanding of its theoretical methods. It will also appeal to experimentalists searching for a rigorous but accessible treatment of the theory in the area.

Section I Preliminaries

Introduction

Quantum Mechanics: instructions for use

Section II Foundations

Gaussian States of continuous variable systems

Phase Space methods

Section III Dynamics

Gaussian Operations

Diffusive dynamics and continuous monitoring

Section IV Correlations

Entanglement of continuous variable systems

Section V Technologies

Quantum information protocols with continuous variables

A grand tour of continuous variable platforms

Appendices

A note on fermions

Some notable facts about the symplectic group

The Wiener process

Selected mathematical lore on quantum channels

Classical and quantum Cramer Rao bounds

Alessio Serafini earned his PhD from the University of Salerno. He is currently a Reader at University College London. His research focuses mainly on quantum optics, quantum information with continuous variables, and the theory of quantum control.